You can still buy a centrifugal railway, although it will
not be as elegant as the one below from Miami University. Today, to
avoid the forbidden word centrifugal, we use names like "loop-the-loop".
The 1916 Knott catalogue description of a similar piece of apparatus is
illuminating: "Centrifugal Railway, illustrating the opposition
offered by a moving body to any influence exerted to counteract its tendency
to move in a straight line. This apparatus consists of a looped circular
railway down which a body may roll unobstructed. At one point in the loop
illustrated, the body is held by centrifugal force against the underside
of the track in opposition to the force of gravity." This description suggests
the bogus idea of equilibrium so beloved of introductory students, and
misses the point that if the starting point is chosen properly, the body
will actually be in momentary free fall at the highest point of the loop.

This example was made by James W. Queen of Philadelphia,
and is described in the 1881 as being "four feet long, of neatly japanned
tin, on a wooden base with leveling screws and glass ball .. $8.00 ."

The centrifugal railway below is at the University of Texas
at Austin, and was also made by Queen. It has been used constantly for
demonstrations and over the years it has been reworked, with the rails
being replaced by brass strips.

The tin-plate railway below is not a true centrifgal railway,
but does show that the speed of the marble increases in the valleys and
decreases at the peaks. It probably started its life as a child's toy ca.
1900, and is now in the collection at the University of Cincinnati.